Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
U.S. Census Bureau
Human Population Dynamics
The Mathematical Art of M.C. Escher
The Man Who Makes Sense of Numbers
According to U.S. census estimates, the population of Texas grew from 17,045,000 people in 1990 to 18,378,000 in 1994. The population of Massachusetts grew from 6,018,000 people in 1990 to 6,041,000 people in 1994.
If the population figures above were difficult for you to read and absorb, you're not alone. Reading about data can be awkward. When it's presented like this, it's hard to grasp the essential information and to see the important messages that may be behind the numbers. If this information were presented as a chart or, better yet, as a picture, it would be much easier to understand.
Charts and tables
Let's try presenting the population figures above as a table.
The table allows you to scan for important points more easily. Now we can easily see that both Texas and Massachusetts experienced a growth in population between 1990 and 1994. We can also see that Texas has a much larger population than Massachusetts. What else is hiding in this data, though? What else can we learn?
Pictures of information
By presenting these same population figures as a picture, we can learn still more about population growth in these two states. Take a look at these two simple bar graphs that represent the data above:
The bar graph makes the messages in the data much more visible. You can easily see, for example, that the population of Texas grew faster than that of Massachusetts during those years. The bar graph gives you new clues about the information. It shows you patterns that you might not notice in a text or table format.
Getting the message across
Clear charts and graphics may be more important than you think. They aren't just used for sales pitches and in annual company reports. Pictures of information are used in decision making in a variety of fields: air travel, government legislation, manufacturing and industry, education, and many others. In some cases, being able to rapidly read and interpret information can be a matter of life and death.
Edward Tufte, a Yale University professor, suggests that "chart junk" (misleading or unclear graphics, charts, and tables) can sometimes have disastrous effects. For example, he believes that the crash of the space shuttle Challenger could have been avoided if the decision-making team had had better information available to them. Because their charts did not convincingly represent a serious problem with the way one of the shuttle's parts would react to low temperatures, the decision makers made a fatal call: they allowed the shuttle to launch. When the shuttle was launched in very cold weather29 degrees Fahrenheitthe crucial part failed. The Challenger burst into flames.
You've probably heard the saying, "A picture is worth a thousand words." This saying expresses mathematical thinking very well. Mathematics tries to reduce, distill, and present information so that problems can be more easily solved, and tables and graphs are a popular way to do that. Every day in sales meetings, courtrooms, and classrooms, these pictures of information allow people to communicate more effectivelyand, hopefully, to make informed decisions.